I don't think the Beatles song really tells us much about 'cottagecore' or rural life in the 1800s.

Retirees in the 1960s were not aspiring to a rural way of life, or giving up plumbing or electricity. They were just buying a small house suitable for two older people to live in together.

This was a middle class goal with very little overlap to today's 'cottagecore' other than the word 'cottage'.